MinT - Information on Result #848313

Information on Result #848313

Linear OOA(8⁸⁵, 45, F₈, 2, 68) (dual of [(45, 2), 5, 69]-NRT-code), using OOA 2-folding based on linear OA(8⁸⁵, 90, F₈, 68) (dual of [90, 5, 69]-code), using

juxtaposition [i] based on
1. linear OA(8¹⁵, 20, F₈, 12) (dual of [20, 5, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁵, 23, F₈, 12) (dual of [23, 8, 13]-code), using
    - algebraic-geometric code AG(F,10P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]
2. linear OA(8⁶⁵, 70, F₈, 55) (dual of [70, 5, 56]-code), using
  - constructionÂ X applied to AG(F,10P) âŠ‚ AG(F,13P) [i] based on
    1. linear OA(8⁶¹, 64, F₈, 55) (dual of [64, 3, 56]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using the Suzuki function field over F₈ [i]
    2. linear OA(8⁵⁹, 64, F₈, 50) (dual of [64, 5, 51]-code), using algebraic-geometric code AG(F,13P) with known gap numbers [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
    3. linear OA(8⁴, 6, F₈, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,8)), using
      - discarding factors / shortening the dual code based on linear OA(8⁴, 8, F₈, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,8)), using
        Reedâ€“Solomon code RS(4,8) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.